Statistics: Final Project Report Chipotle Water Cup: Water or Soda?

Transcription

1 Statistics: Final Project Report Chipotle Water Cup: Water or Soda? Introduction: For our experiment, we wanted to find out how many customers at Chipotle actually get water when they order a water cup. We chose Chipotle because Chipotle is a very popular fast-food restaurant and almost everyone has heard of Chipotle, or enjoys eating it. We wanted to find out if more people get soda with water cups than actual water. In observing this, we saw if the customers at Chipotle chose the healthier option (water) and also saw if people just asked for water cups because they didn t want to pay for an actual soda cup or soda bottle. From eating at Chipotle numerous times, we also knew that Chipotle does in fact give out free water cups to their customers when they ask. Data Collection: The population we studied were the customers at three of our local Chipotle restaurants. We studied the proportion of the customers who get a water cup vs those who do not get a water cup. We also looked at the proportion of those who get a water cup, how many of them actually got water (rather than soda). We took a systematic random sample of the customers at each of these locations. Every third person that was waiting in the line was sampled. Two of us sat at a table by the end of the line and counted every third person in line and observed who asked for a water cup and who did not. The remaining two members of our group sat by the soda dispenser and counted which of these people actually obtained water in their water cups or if they got soda instead (the people in line were also visible to our group members sitting by the soda dispenser, so they knew which people to make note of getting soda or water). We used a systematic random sample because the other options were not practical for our experiment. The systematic random sample was the most efficient way to collect our data of those who were waiting in line at the various Chipotles. There was little bias in our experiment because we went to three different chipotles, bound to have different customers, and we went at the same time of day to each of the Chipotles (5 p.m.-6 p.m.). We went on different days of the week as well so there would be no bias to one particular day. # of customers being sampled who were sampled) who got a water cup who got a water cup) who actually got water Chipotle #1 Chipotle #2 Chipotle #3 Totals

2 Data Report: # of customers being sampled who were sampled) who got a water cup who got a water cup) who actually got water Chipotle # Chipotle # Chipotle # Totals Chipotle 1 34% Water Cup No Water Cup 66% Chipotle 2 60% 40% Water Cup No Water Cup

3 Chipotle 3 26% Water Cup No Water Cup 74% Chipotle 1 67% 33% Proportion customers (of those who got a water cup) who actually got water Proportion of customers (of those who got a water cup) who got soda

4 Chipotle 2 43% 57% Proportion customers (of those who got a water cup) who actually got water Proportion of customers (of those who got a water cup) who got soda Chipotle 3 56% 44% Proportion customers (of those who got a water cup) who actually got water Proportion of customers (of those who got a water cup) who got soda

5 who got a water cup) who actually got water Getting Water or Not at Chipotle Chipotle 1 Chipotle 2 Chipotle 3 -- Summary statistics -- For the customers who got a water cup: Standard deviation of the sample ( )² + ( )² + ( )² = /2 = = Min - 9 Max - 14 p = 35/105 =.33 n = 105 For the customers who actually got water: Standard deviation of the sample (4-5.33)² + (8-5.33)² + (4-5.33)² = /2 = = Min - 4 Max - 8 p = 16/35 =.4571 n = 35

6 Inference Significance Test: Hypothesis Test H0: p =.30 where p is the proportion of Chipotle customers who actually get water when they order a water cup. Ha: p >.30 Conditions: Random: Yes, we took a systematic random sample of the customers at each of the Chipotles. Normal: Yes, np 10 = 35(16/35) = 16, n(1-p) 10 = 35(1-(16/35)) = 19 Independent: The observations (customer s preferences) are independent of each other and N > 10(n) = 10(35) = 350 In calc: 1 Proportion Z Test po:.30 x: 16 n: 35 Prop >.30 z = p =.0212 p =.4571 n = 35 Conclusion: p <.05 so we reject the null hypothesis. There is enough convincing evidence to conclude that the proportion of Chipotle customers who actually get water when they order a water cup is greater than 30%. Overall Conclusion: The total number of customers sampled at all three Chipotle locations was 105, the number of customers who got a water cup was 35, and the number of customers who actually got water was 16. P turned out to be.0212 which is less than.05, so we reject the null hypothesis (p=.30) and we could conclude that the proportion of Chipotle customers who actually get water when they order a water cup is greater than 30%, although a significant amount of customers get soda at Chipotle when they say they ll get water. There may have been bias because teenagers are more likely to get soda rather than water compared to adults who eat Chipotle. Also, if people are taking their food to-go, they may already have water or soda at home so there is no need to get a water cup. The data could be biased because more students go to Chipotle more on the weekends because they re too busy studying during the weekdays. For further study, we could go to more Chipotle locations, perform the survey at different times of the day, and get a bigger sample size. Sometimes it was difficult to observe what drink the customers were getting, so if we were to repeat this, we would be closer to the soda/drink machine.